A mathematical theory of gapless edges of 2d topological orders. Part I

Understand

This is the first part of a two-part work on a unified mathematical theory of gapped and gapless edges of 2d topological orders.

• We analyze all the possible observables on the 1+1D world sheet of a chiral gapless edge of a 2d topological order, and show that these observables form an enriched unitary fusion category, the Drinfeld center of which is precisely the unitary modular tensor category associated to the bulk.
• This mathematical description of a chiral gapless edge automatically includes that of a gapped edge (i.e.
• a unitary fusion category) as a special case.